I would think that 2-3 feet should be sufficient. You just don't want them getting too much N so that they put on more foliage than beans. Any additional P or K would be fine. If you have to crowd them less than 2 feet I would plant something next to them that also has lower N requirements like other legumes or tomatoes, ect.

Fertilizer can travel as far as water can. And generally, water does not travel horizontally very far.

What you can do is to put a plastic barier , similar to what they use between grass and garden beds. They are about 6-8" wide and come in rolls, sold at garden center @ HD and elsewhere. Alternatively, you can use a 9/16 x 6" cedar board, the ones are used to make fence with.
As I said, water tends to go down by the force of gravity. UNLESS the bed is flooded.

Also depends on the type of fertilizer. Water souable fertilizers will spread/dissipate out further than a dry granular one will even when it gets wet.

Ideally legumes should be planted as far away from routinely fertilized crops as possible - like a separate area - but that isn't always practical. When it isn't then choose granular supplements rather than liquids or as suggested, some sort of barrier between.

Many gardeners use flowers or other run-off trapping crops between the crops with very different needs but if your space is really limited then that would be a waste of space.

Dave